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Fluid Mechanics - Coggle Diagram
Fluid Mechanics
Hydrostatics
Absolute and pressure and gauge pressure: The gauge pressure is the pressure in relation to the ambient/atmospheric pressure. The absolute pressure is the pressure relative to pressure zero (no air)
Pressure force: F= pA
Pressure force affecting fluid element: Think of this as the net forc on a fluid. These forces that normaly affect liquid is pressure, weight and viscosity.
The forve form gravity and viscosity is zero we have the an equation for hydrostatic which is a function of density, acceleration (gravity) and heigh/depth
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Napla is vector differential operator.
napla p is perpendicular towards constant pressure surface p and indicates the gradient (direction and rate of change)
Pressure increases to the direction of acceleration (if everything is stationary, the acceleration is down).
Free surface of the liquid is perpendicular to the pressure gradient (if stationary
system, the free surface is horizontal)
Buoyancy: The force acting ona submerged body is equal to the weight of the displaced liquid. The fun thing about this is that the bounce force can be writen as the weight of the displaced fluid
Stability: This refers to when a body that floting on a fluid is stable, or in other words not rotating.
First: calculate the basic floting position. In addition, find out the center of gravity and center of buayancy B.
The body is tilted by a smal angle, and new water lin is established, the new position for the center of buayancy is calculated. A verticle line drawn through new buoyancy point and it intersects the symmetry line at the metacenter (point M)
If point M is above the center of mass (positice metacentri height), the body return to the original position, the boyd is stable.
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If the point M is below the center of mass (negative metacentric height), the body will oveerturn, the body is unstable
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Volume and mass flow
Steady state: Irrespective of time, in the problem nothing changes with respect to time. Things llike mass flows, temperatures, control volume size, density all remains constant
Incompressibel flow: This is when density is costant. Liquids are incompressible. For gases, the density might vary, for example if the temperature or pressure changes. Also if gas flow velocity is high, the density changes must be accounted for (compressible gas dynamic)
Mass flow is defined by the velocity normal to the sruface. W is the velocut of the fluid and Wn is the velocity normal to the surface.
Wcos(theta) = Wn or
Wn (dot product with the normal vector of the surface)
During time dt through the srucface dA goes a vole flow dV
dV = (wn) dA dt
volume flow
dV/dt = (Wn) dA or
qv = integral (W*n) dA
This is general form, when the density, velocity and area are not constant. If the problem is stationary (everything is constant) the mass flow would be
qm = pWA (p = density)
voluem flow
qv = WA
Reynolds transport theorem: B is the fluid property (mass, energy, momentum, enthalpy, etc)
b is the amount of B in a differential mass unit
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Linear momentum equation: This whne we use Newton's second law (F= ma) with Reynolds trasnpot theorem
Remeber:
Velocity is with respect to a stationary or zero acceleration coordinate system
ΣF is the vector sum of all the forces affecting the system. The system can be considered as a free-body object, and one must include all surface forces (pressure force, gravity, electro magnetic forces, etc)
The whole equation is vector equation
If the flow dischargers to ambient pressure as sub sonic, the fluid pressure is equal to the ambient
pressure
If possible, choose inlets and outlets so that they are perpendicular to the flow.
Earlier it was noted that the linear momentum equation, as presented previously, only works if the motion is steady with respect to the coordinate system. An example of an accelerating coordinate system is Coriolis acceleration.
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Angular Momentum: Now a moment of a force can be expressed as vectors. The cross porduct between the radius and Force. This the same for the angular momentum
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Praticla Implications of angular momentum equation:
Turbomachinery: pump, compressors, turbines and fans
Irrigation and sprinkler systems
Centrifugal pump:
Radial (normal) velocity. Radial velocity doesn't contribute to momentum. It is used in mass flow calculations, and in the design it used to assesss the bldae height b.
For steady incompressibel flow, the coservation of mass can be expressed as
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